Uniqlo, short for "unique clothing," has been around since 1984 (though it started as a much smaller venture), and really expanded in 2005.

It's focused heavily on the Asian mainland, where markets are growing rapidly, but Uniqlo parent company Fast Retailing Co. knows that in order to dominate worldwide, it needs to have a significant presence in the U.S. and Europe.

Chief Executive Tadashi Yanai summarized the company's current strategy: "We have to become the No. 1 in Asia to eventually become the global No. 1."

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Uniqlo started out as a small Japanese menswear chain in 1949

Image: AP

Fast Retailing CEO and president Tadashi Yanai expanded his father Hitoshi's tailoring business Men's Shop Ogori Shōji, which had been around since 1949, by adding a casual store for both men and women.

In 1984, Yanai branded the new store concept "Unique Clothing Company," or "Uniqlo" for short. By 1991, he renamed its parent company Fast Retailing.

The company went public in 1994, and soon rolled out several hundred stores across Japan

By 1994, the company went public on the Hiroshima Stock Exchange. In 1999, it was listed on the Tokyo Stock Exchange -- by then, it had 357 stores throughout Japan.

Around that time, Uniqlo pushed into popularity through its fleece wear, which it offered in a mix of vibrant color options (51 shades by 2000) and creative marketing, including a store in the trendy Harajuku district of Japan.

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In the early 2000s, Uniqlo hit a wall when it couldn't differentiate itself in the oversaturated Japanese market and from other retailers in the UK

In 2002 and 2003, Uniqlo saw the market become saturated with fleece products, which up until then were the brand's calling card.

This didn't help its entry into the European market. Uniqlo had to close 16 out of 21 new British stores -- which it blamed on the high rent and staffing costs of running a UK store, but also tepid interest from British consumers, who couldn't see how Uniqlo differentiated itself from other products on the market.

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But by 2004, Fast Retailing's sales rebounded 50%, thanks to tighter inventory control and a retrained focus on women's clothing

Rather than start by opening an American flagship, the New Jersey Uniqlos were designed to "to be your neighbor, where you go regularly for your everyday fashion basics."

The Uniqlos launched in the middle of a European casual-wear explosion in the U.S., with H&M and Zara's also making heavy investments in the American market. H&M currently has 200 U.S. stores to Uniqlo's one, but the two chains have undertaken incredibly different strategies. H&M's saturation has made it far less of a trendy, exciting concept than Uniqlo.

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But the concept still wasn't resonating in the West, so the company rebranded itself as a provider of "basics"

Rebranding efforts began in 2005 after the UK and inaugural U.S. stores continued to underperform.

According to New York magazine, "Yanai hired a creative team to rebrand the company abroad, including Kashiwa Sato of Samurai, Masamichi Katayama of Wonderwall, and Markus Kiersztan of MP Creative. The relaunch of Uniqlo would start with the New York store."

The piece also quotes Kiersztan as saying, "Uniqlo is the brand that happens in a nonexisting space," which explains much of the store's appeal. Rather than catering toward social trends or movements in taste, the clothes fulfill basic needs at a high quality.

Another benchmark came in 2009, when the store partnered with German ex-Prada designer Jil Sander for a line of clothing called J+. The collaboration, which ended in June, produced a product that nodded toward high fashion but stayed within a reasonable price range, benefitting both Uniqlo and Sander.

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With its new model, Uniqlo opened flagship stores in Tokyo, New York, and Paris

Now there are 1020 Uniqlo stores -- most are still in Japan

This breaks down to approximately 840 in Japan and 140 elsewhere in the world -- though about 95 of those are in China and South Korea. Sales are estimated at $13 billion (one trillion yen) for the current fiscal year. But, if all goes according to plan, these numbers will increase very soon.

Fast Retailing Co. also says the two locations will create 1,100 jobs for New York -- though Crain's New York Business says these jobs will be almost entirely part-time positions, which inflate employment numbers and don't allow benefits or overtime.

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Beyond New York, the goal is to create 4,000 stores worldwide by 2020

The goal for Fast Retailing's total sales in the fiscal year ending August 2015 is $22 billion, spread among 4,000 Uniqlo stores worldwide, as well as from the company's other assets (which include Theory, Comptoir des Cotonniers, and g.u.).

As lofty as this all might seem, the only two-decade-old Uniqlo's rapid growth in the past means that, as long as Americans outside of New York City take to the brand, it could very well be truly dominant by 2020.